2.3.255 Problems 25401 to 25500

Table 2.1053: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25401

11923

\begin{align*} y^{\prime }&=\frac {y}{\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )+1} \\ \end{align*}

64.157

25402

11450

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 y x -1\right )&=0 \\ \end{align*}

64.220

25403

12463

\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (a +x \right ) y&=0 \\ \end{align*}

64.221

25404

13500

\begin{align*} y y^{\prime }-y&=A x +\frac {B}{x}-\frac {B^{2}}{x^{3}} \\ \end{align*}

64.253

25405

13425

\begin{align*} y^{\prime }&=\lambda \arcsin \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\ \end{align*}

64.296

25406

2937

\begin{align*} y x +\left (y+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

64.300

25407

6088

\begin{align*} \left (\operatorname {c0} \,x^{2}+\operatorname {b0} x +\operatorname {a0} \right ) y+a x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

64.362

25408

22386

\begin{align*} y&=\left (2 x +3 y\right ) y^{\prime } \\ \end{align*}

64.397

25409

13557

\begin{align*} y y^{\prime }&=\frac {y}{\sqrt {a x +b}}+1 \\ \end{align*}

64.428

25410

5684

\begin{align*} 2 \left (1+y\right )^{{3}/{2}}+3 y^{\prime } x -3 y&=0 \\ \end{align*}

64.575

25411

6198

\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}

64.577

25412

5429

\begin{align*} {y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3}&=0 \\ \end{align*}

64.583

25413

788

\begin{align*} 2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\ \end{align*}

64.687

25414

3231

\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +3 y&=\left (x -1\right ) \ln \left (x \right ) \\ \end{align*}

64.730

25415

23867

\begin{align*} y^{\prime }&=\frac {3 x -y}{x +2 y} \\ \end{align*}

64.766

25416

2514

\begin{align*} 2 t \cos \left (y\right )+3 t^{2} y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

64.770

25417

25215

\begin{align*} t \left (t^{2}-4\right ) y^{\prime \prime }+y&={\mathrm e}^{t} \\ y \left (1\right ) &= y_{1} \\ y^{\prime }\left (1\right ) &= y_{1} \\ \end{align*}

64.867

25418

24162

\begin{align*} v^{2}+x \left (x +v\right ) v^{\prime }&=0 \\ \end{align*}

64.884

25419

4988

\begin{align*} 2 x^{3} y^{\prime }&=y \left (x^{2}-y^{2}\right ) \\ \end{align*}

64.910

25420

5349

\begin{align*} x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y&=0 \\ \end{align*}

64.918

25421

11927

\begin{align*} y^{\prime }&=-\frac {x^{2} \left (a x -2 \sqrt {a \left (a \,x^{4}+8 y\right )}\right )}{2} \\ \end{align*}

65.023

25422

17102

\begin{align*} y^{\prime }&=y^{3}-1 \\ \end{align*}

65.119

25423

12580

\begin{align*} x \left (x^{2}-1\right ) y^{\prime \prime }+\left (3 x^{2}-1\right ) y^{\prime }+y x&=0 \\ \end{align*}

65.150

25424

23878

\begin{align*} y^{\prime }&=\frac {2 y^{3}+2 x^{2} y}{x^{3}+2 x y^{2}} \\ \end{align*}

65.150

25425

5117

\begin{align*} \left (a x +b y\right ) y^{\prime }+x&=0 \\ \end{align*}

65.160

25426

14477

\begin{align*} x +2 y+\left (2 x -y\right ) y^{\prime }&=0 \\ \end{align*}

65.242

25427

17292

\begin{align*} 1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }&=0 \\ \end{align*}

65.328

25428

13549

\begin{align*} y y^{\prime }-y&=\frac {k}{\sqrt {A \,x^{2}+B x +c}} \\ \end{align*}

65.332

25429

21449

\begin{align*} y^{2}+\left (3 y x -1\right ) y^{\prime }&=0 \\ \end{align*}

65.361

25430

17929

\begin{align*} x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime }&=0 \\ \end{align*}

65.454

25431

2521

\begin{align*} y^{\prime }&=y^{2}+\cos \left (t \right )^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}

65.473

25432

14043

\begin{align*} \left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\ \end{align*}

65.500

25433

13615

\begin{align*} y y^{\prime }&=a x \cos \left (\lambda \,x^{2}\right ) y+x \\ \end{align*}

65.520

25434

12472

\begin{align*} x^{2} y^{\prime \prime }+\left (2 a x +b \right ) x y^{\prime }+\left (a b x +c \,x^{2}+d \right ) y&=0 \\ \end{align*}

65.575

25435

14478

\begin{align*} 3 x -y-\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}

65.612

25436

5232

\begin{align*} \left (x +y\right )^{2} y^{\prime }&=\left (x +y+2\right )^{2} \\ \end{align*}

65.618

25437

14439

\begin{align*} 3 x +2 y+\left (2 x +y\right ) y^{\prime }&=0 \\ \end{align*}

65.685

25438

19238

\begin{align*} y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\ \end{align*}

65.835

25439

12516

\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\ \end{align*}

65.870

25440

6453

\begin{align*} y y^{\prime \prime }&=c y^{2}+b y y^{\prime }+a {y^{\prime }}^{2} \\ \end{align*}

65.887

25441

14028

\begin{align*} x y^{2} \left (y^{\prime } x +3 y\right )-2 y+y^{\prime } x&=0 \\ \end{align*}

65.993

25442

20319

\begin{align*} y^{\prime }&=\sin \left (x +y\right )+\cos \left (x +y\right ) \\ \end{align*}

66.023

25443

12634

\begin{align*} y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (-a^{2}-\lambda \left (x^{2}-1\right )\right ) y}{\left (x^{2}-1\right )^{2}} \\ \end{align*}

66.071

25444

13341

\begin{align*} y^{\prime }&=y^{2}-\lambda ^{2}+3 a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \\ \end{align*}

66.138

25445

21822

\begin{align*} \left (x^{2}+y^{2}\right ) \left (y^{\prime } x +y\right )&=x y \left (-y+y^{\prime } x \right ) \\ \end{align*}

66.152

25446

12078

\begin{align*} y^{\prime }&=\frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+3 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+9 y} \\ \end{align*}

66.175

25447

12044

\begin{align*} y^{\prime }&=-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (x +1\right )} \\ \end{align*}

66.183

25448

5014

\begin{align*} y^{\prime } \sqrt {b^{2}+x^{2}}&=\sqrt {y^{2}+a^{2}} \\ \end{align*}

66.302

25449

12522

\begin{align*} x \left (x -1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\ \end{align*}

66.313

25450

4877

\begin{align*} x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2}&=0 \\ \end{align*}

66.458

25451

14068

\begin{align*} \left (x -y^{\prime }-y\right )^{2}&=x^{2} \left (2 y x -x^{2} y^{\prime }\right ) \\ \end{align*}

66.469

25452

22376

\begin{align*} U^{\prime }&=\frac {U+1}{\sqrt {s}+\sqrt {s U}} \\ \end{align*}

66.487

25453

8734

\begin{align*} y^{\prime }&=\frac {3 x -y+1}{2 x +y+4} \\ \end{align*}

66.490

25454

11847

\begin{align*} f \left (x^{2}+y^{2}\right ) \sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x +y&=0 \\ \end{align*}

66.588

25455

7411

\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}

66.644

25456

1165

\begin{align*} y^{\prime }&=\frac {3 y^{2}-x^{2}}{2 y x} \\ \end{align*}

66.687

25457

6084

\begin{align*} -\left (k -p \right ) \left (1+k +p \right ) y-2 \left (1+k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

66.722

25458

19114

\begin{align*} {y^{\prime }}^{3}+y^{3}-3 y y^{\prime }&=0 \\ \end{align*}

66.815

25459

11644

\begin{align*} y^{\prime } \cos \left (y\right )+x \sin \left (y\right ) \cos \left (y\right )^{2}-\sin \left (y\right )^{3}&=0 \\ \end{align*}

66.856

25460

2949

\begin{align*} \left (2 x +3 x^{2} y\right ) y^{\prime }+y+2 x y^{2}&=0 \\ \end{align*}

67.036

25461

21325

\begin{align*} -x^{\prime \prime }+x&={\mathrm e}^{-x} \\ x \left (a \right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align*}

67.083

25462

5528

\begin{align*} \left (-a^{2}+1\right ) x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -a^{2} x^{2}+y^{2}&=0 \\ \end{align*}

67.171

25463

14713

\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=4 \ln \left (x \right ) \\ \end{align*}

67.207

25464

11748

\begin{align*} \left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2}&=0 \\ \end{align*}

67.407

25465

15822

\begin{align*} S^{\prime }&=S^{3}-2 S^{2}+S \\ S \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}

67.544

25466

24305

\begin{align*} y \left (y^{2}-3 x^{2}\right )+x^{3} y^{\prime }&=0 \\ \end{align*}

67.584

25467

13316

\begin{align*} y^{\prime }&=y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} {\mathrm e}^{2 \lambda \,x^{2}} \\ \end{align*}

67.698

25468

24155

\begin{align*} \left (x -y\right ) \left (4 x +y\right )+x \left (5 x -y\right ) y^{\prime }&=0 \\ \end{align*}

67.746

25469

23904

\begin{align*} x^{3}+y^{2}+\left (y x -3 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

67.807

25470

17065

\begin{align*} y^{\prime }&=-\frac {t}{y} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

67.829

25471

13981

\begin{align*} \left (x +y+1\right ) y^{\prime }+1+4 x +3 y&=0 \\ \end{align*}

67.912

25472

5038

\begin{align*} y y^{\prime }+a x +b y&=0 \\ \end{align*}

67.913

25473

20483

\begin{align*} \left (-y+y^{\prime } x \right ) \left (x -y y^{\prime }\right )&=2 y^{\prime } \\ \end{align*}

67.913

25474

23843

\begin{align*} \left (x +y\right ) y^{\prime }&=x -y \\ \end{align*}

67.966

25475

13386

\begin{align*} y^{\prime } x&=a \cos \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cos \left (\lambda x \right )^{m} \\ \end{align*}

67.987

25476

6171

\begin{align*} \left (b x +a \right ) y+2 \left (1-2 x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}

68.017

25477

25528

\begin{align*} m y^{\prime \prime }+k y&=1 \\ \end{align*}

68.132

25478

25891

\begin{align*} 3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\ \end{align*}

68.159

25479

19092

\begin{align*} y^{\prime } \left (x^{2}+y^{2}+3\right )&=2 x \left (2 y-\frac {x^{2}}{y}\right ) \\ \end{align*}

68.247

25480

23888

\begin{align*} \frac {8 x^{4} y+12 x^{3} y^{2}+2}{2 x +3 y}+\frac {\left (2 x^{5}+3 x^{4} y+3\right ) y^{\prime }}{1+x^{2} y^{4}}&=0 \\ \end{align*}

68.326

25481

19903

\begin{align*} \left (3 x +4 y\right ) y^{\prime }+y-2 x&=0 \\ \end{align*}

68.398

25482

6330

\begin{align*} b y+a \left (-1+y^{2}\right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

68.565

25483

13655

\begin{align*} y^{\prime }&=\frac {y^{3}}{\sqrt {a \,x^{2}+b x +c}}+y^{2} \\ \end{align*}

68.627

25484

13502

\begin{align*} y y^{\prime }-y&=A +B \,{\mathrm e}^{-\frac {2 x}{A}} \\ \end{align*}

68.649

25485

22020

\begin{align*} y^{\prime }&=\frac {y^{2}}{y x +\left (x y^{2}\right )^{{1}/{3}}} \\ \end{align*}

68.860

25486

9059

\begin{align*} y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\ \end{align*}

68.958

25487

14466

\begin{align*} v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime }&=0 \\ \end{align*}

68.997

25488

5198

\begin{align*} \left (1-x^{3} y\right ) y^{\prime }&=y^{2} x^{2} \\ \end{align*}

69.082

25489

20012

\begin{align*} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3}&=0 \\ \end{align*}

69.106

25490

23219

\begin{align*} y^{\prime }&=\frac {y-x +1}{3 x -y-1} \\ \end{align*}

69.130

25491

14329

\begin{align*} x^{\prime \prime }+t^{2} x^{\prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

69.247

25492

23290

\begin{align*} \sin \left (x \right ) y^{\prime \prime }+y^{\prime } x +y&=2 \\ y \left (\frac {3 \pi }{4}\right ) &= 1 \\ y^{\prime }\left (\frac {3 \pi }{4}\right ) &= 1 \\ \end{align*}

69.351

25493

24270

\begin{align*} y^{2}-x \left (2 x +3 y\right ) y^{\prime }&=0 \\ \end{align*}

69.497

25494

17654

\begin{align*} 9 x^{2} y^{\prime \prime }+27 y^{\prime } x +10 y&=\frac {1}{x} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}

69.690

25495

14470

\begin{align*} \sqrt {x +y}+\sqrt {x -y}+\left (\sqrt {x -y}-\sqrt {x +y}\right ) y^{\prime }&=0 \\ \end{align*}

69.742

25496

10322

\begin{align*} y^{\prime }&=\left (\pi +x +7 y\right )^{{7}/{2}} \\ \end{align*}

69.816

25497

1681

\begin{align*} 3 \cos \left (x \right ) y+4 x \,{\mathrm e}^{x}+2 x^{3} y+\left (3 \sin \left (x \right )+3\right ) y^{\prime }&=0 \\ \end{align*}

69.853

25498

25217

\begin{align*} y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y&=f \left (t \right ) \\ \end{align*}

69.872

25499

24326

\begin{align*} 3 \sin \left (y\right )-5 x +2 x^{2} \cot \left (y\right ) y^{\prime }&=0 \\ \end{align*}

69.962

25500

21549

\begin{align*} a_{0} \left (x \right ) y^{\prime \prime }+a_{1} \left (x \right ) y^{\prime }+a_{2} \left (x \right ) y&=f \left (x \right ) \\ \end{align*}

70.091